Stocks problem

[gmat009]

Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?
A. k/m %
B. (k – m) %
C. [100(k – m)] / (100 + k) %
D. [100(k – m)] / (100 + m) %
E. [100(k – m)] / (100 + k + m) %

OA is D

Plz. explain this problem

[stop@800]

let
old price = P
old earning = E

new price = P(1+ k /100)
new earnings = E(1+ k /100) Error!!

Edited:
new earnings = E(1+ m /100)

% increase =

[ (new price)/(new earnings) - (old price)/(old earnings) ] / ((old price)/(old earnings))

Substitute and solve for ratio

You will easily get D

Let me know if you need more detailed explanation.....

Hope this helps!!

[4meonly]

let
old price = P
old earning = E

new price = P(1+ k /100)
new earnings = E(1+ k /100)

% increase =

[ (new price)/(new earnings) - (old price)/(old earnings) ] / ((old price)/(old earnings))

Substitute and solve for ratio

You will easily get D

Let me know if you need more detailed explanation.....

Hope this helps!!

Could you please elaborate.
I think I made a mistake somewhere and not able to arrive to correct answer
thanx

[stop@800]

You want me to explain which step?

I think may be u want me to explain
new price = P(1+ k /100)

K% increase is actually increase by k/100 fraction
so increase is PK/100
new price = price + increase
P + PK/100

Please let me know if i missed something.

[4meonly]

I have some problems with this

[ (new price)/(new earnings) - (old price)/(old earnings) ] / ((old price)/(old earnings))
Substitute and solve for ratio
You will easily get D

I think I made some stupid mistake in calculations - can you please post step-by-step calculations?
thanx!

[Stockmoose16]

You want me to explain which step?

I think may be u want me to explain
new price = P(1+ k /100)

K% increase is actually increase by k/100 fraction
so increase is PK/100
new price = price + increase
P + PK/100

Please let me know if i missed something.

Can you explain why my reasoning is wrong?

I tried to input numbers:

Starting P/E ratio 2:1, ending P/E ratio: 5:2

That means K: 50% and M: 20%... the overall increase in P/E ratio is:

(2.5-2)/2= 25%

None of the answer choices give me 25%....

In addition, I noticed you started changing the numbers into fractions (i.e. k/100), but the question clearly states K%, not K/100%. I don't understand why/how you decided to solve using fractions. Can you explain what's wrong with my example above and also why you went from K% to K/100%?

[stop@800]

I have some problems with this

[ (new price)/(new earnings) - (old price)/(old earnings) ] / ((old price)/(old earnings))
Substitute and solve for ratio
You will easily get D

solving numerator.........

P(1+k/100) / E(1+m/100) - P/E

P(100+k) / E(100+m) - P/E

P/E ( (100+k/100+m) - 1 )

P/E (100+k-100-m)/(100+m)

P/E (k- m)/(100+m)

now we need to divide this by p/e
so we have

(k- m)(100+m)

now adding %

100(k- m)/(100+m) %


PS:
In my earlier post i have written
new earnings = E(1+ k /100)
it shud be
instead new earnings = E(1+ m /100)

I think I made some stupid mistake in calculations - can you please post step-by-step calculations?
thanx!

[stop@800]

You want me to explain which step?

I think may be u want me to explain
new price = P(1+ k /100)

K% increase is actually increase by k/100 fraction
so increase is PK/100
new price = price + increase
P + PK/100

Please let me know if i missed something.

Can you explain why my reasoning is wrong?

I tried to input numbers:

Starting P/E ratio 2:1, ending P/E ratio: 5:2

That means K: 50% and M: 20%... the overall increase in P/E ratio is:

How you got 50% ??

(2.5-2)/2= 25%

None of the answer choices give me 25%....

In addition, I noticed you started changing the numbers into fractions (i.e. k/100), but the question clearly states K%, not K/100%. I don't understand why/how you decided to solve using fractions. Can you explain what's wrong with my example above and also why you went from K% to K/100%?

in increase by K% is increase by a fraction of K/100

Ex:
increase of 15% is increase by a fraction 15/100 = .15

so for Rs. 200 increase of 15% = increase by 200*.15 = 30

and new value will be 200+30
ie
for P old value
increase is PK/100
and
new value = P + PK/100

Hope this helps!!

[Stockmoose16]

You want me to explain which step?

I think may be u want me to explain
new price = P(1+ k /100)

K% increase is actually increase by k/100 fraction
so increase is PK/100
new price = price + increase
P + PK/100

Please let me know if i missed something.

Can you explain why my reasoning is wrong?

I tried to input numbers:

Starting P/E ratio 2:1, ending P/E ratio: 5:2

That means K: 50% and M: 20%... the overall increase in P/E ratio is:

How you got 50% ??

(2.5-2)/2= 25%

None of the answer choices give me 25%....

In addition, I noticed you started changing the numbers into fractions (i.e. k/100), but the question clearly states K%, not K/100%. I don't understand why/how you decided to solve using fractions. Can you explain what's wrong with my example above and also why you went from K% to K/100%?

in increase by K% is increase by a fraction of K/100

Ex:
increase of 15% is increase by a fraction 15/100 = .15

so for Rs. 200 increase of 15% = increase by 200*.15 = 30

and new value will be 200+30
ie
for P old value
increase is PK/100
and
new value = P + PK/100

Hope this helps!!

Sorry, I gave a bad example... now, using the correct numbers, you'll see that my method seems to work. I still don't understand your methodology. Why are you changing things into fractions when the question clearly states: "Stock X increased by K percent." It does not say, "Stock A increased by K/100%." Here's the way I did the problem:

Starting P/E: 50/100
Ending P/E: 75/120

K: (75-50)/50= 50%
M: (120-100)/120=20%

Percent change in p/e is: (5/8-1/2)/1/2 = 1/8/1/2 = 1/4 = 25%

Now, if you plug into answer choice D:

[100 (k-m)] / (100+m) %

you get:

[100 (50-20)] / 100+20) %

(3000/120)

=25%

Is this logic correct? If so, I still don't understand why you put M and K over 100. The question never asks you to create a fraction. It says it's M%, not M/100 %. Please further explain.

[Stockmoose16]

You want me to explain which step?

I think may be u want me to explain
new price = P(1+ k /100)

K% increase is actually increase by k/100 fraction
so increase is PK/100
new price = price + increase
P + PK/100

Please let me know if i missed something.

Can you explain why my reasoning is wrong?

I tried to input numbers:

Starting P/E ratio 2:1, ending P/E ratio: 5:2

That means K: 50% and M: 20%... the overall increase in P/E ratio is:

How you got 50% ??

(2.5-2)/2= 25%

None of the answer choices give me 25%....

In addition, I noticed you started changing the numbers into fractions (i.e. k/100), but the question clearly states K%, not K/100%. I don't understand why/how you decided to solve using fractions. Can you explain what's wrong with my example above and also why you went from K% to K/100%?

in increase by K% is increase by a fraction of K/100

Ex:
increase of 15% is increase by a fraction 15/100 = .15

so for Rs. 200 increase of 15% = increase by 200*.15 = 30

and new value will be 200+30
ie
for P old value
increase is PK/100
and
new value = P + PK/100

Hope this helps!!

I tried using your equations and didn't get the correct answer. See the following:

(P+PK/100 //E+EM/100) - (P+pm/100 /E +EM/100) // P/E

= P (K-M) / E(100+M) // P/E

= K-m / 100+M

This is not one of the answers. I think something is wrong.

[silentuser]

I tried using your equations and didn't get the correct answer. See the following:

(P+PK/100 //E+EM/100) - (P+pm/100 /E +EM/100) // P/E

= P (K-M) / E(100+M) // P/E

= K-m / 100+M

This is not one of the answers. I think something is wrong.

Sockmoose16:

Your answer is correct. You just need to multiply it by 100 to get the answer in percentage. Then you will get Choice D.